József Solymosi is a Hungarian-Canadian mathematician and a professor of mathematics at the

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

. His main research interests are

arithmetic combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (ad ...

discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geome ...

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

, and

combinatorial number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

Education and career

Solymosi earned his master's degree in 1999 under the supervision of László Székely from the

Eötvös Loránd University Eötvös Loránd University ( hu, Eötvös Loránd Tudományegyetem, ELTE) is a Hungarian public research university based in Budapest. Founded in 1635, ELTE is one of the largest and most prestigious public higher education institutions in Hung ...

and his Ph.D. in 2001 at

ETH Zürich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

under the supervision of

Emo Welzl Emmerich (Emo) Welzl (born 4 August 1958 in Linz, Austria)Curriculum vitae
retrieved 2012-02-11. is ...

. His doctoral dissertation was ''Ramsey-Type Results on Planar Geometric Objects''. From 2001 to 2003 he was S. E. Warschawski Assistant Professor of Mathematics at the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

. He joined the faculty of the University of British Columbia in 2002. He was

editor in chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ...

of the ''

Electronic Journal of Combinatorics The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin (Georgi ...

'' from 2013 to 2015.

Contributions

Solymosi was the first online contributor to the first Polymath Project, set by

Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity Col ...

to find improvements to the

Hales–Jewett theorem In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial ...

. One of his theorems states that if a finite set of points in the

Euclidean plane In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions of ...

has every pair of points at an integer distance from each other, then the set must have a

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...

(largest distance) that is linear in the number of points. This result is connected to the

Erdős–Anning theorem The Erdős–Anning theorem states that an infinite number of points in the plane can have mutual integer distances only if all the points lie on a straight line. It is named after Paul Erdős and Norman H. Anning, who published a proof of it in ...

, according to which an infinite set of points with integer distances must lie on one line. In connection with the related

Erdős–Ulam problem In mathematics, the Erdős–Ulam problem asks whether the plane contains a dense set of points whose Euclidean distances are all rational numbers. It is named after Paul Erdős and Stanislaw Ulam. Large point sets with rational distances The Er ...

, on the existence of dense subsets of the plane for which all distances are rational numbers, Solymosi and de Zeeuw proved that every infinite rational-distance set must either be dense in the

Zariski topology In algebraic geometry and commutative algebra, the Zariski topology is a topology which is primarily defined by its closed sets. It is very different from topologies which are commonly used in the real or complex analysis; in particular, it is n ...

or it must have all but finitely many of its points on a single line or circle. With

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

, Solymosi proved a bound of

(mn)^

on the number of incidences between

n

points and

m

affine subspaces of any finite-dimensional Euclidean space, whenever each pair of subspaces has at most one point of intersection. This generalizes the

Szemerédi–Trotter theorem The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (''i.e.'', the number of point-line pairs, such that the point ...

on points and lines in the Euclidean plane, and because of this the exponent of

2/3

cannot be improved. Their theorem solves (up to the

\varepsilon

in the exponent) a conjecture of Toth, and was inspired by an analogue of the Szemerédi–Trotter theorem for lines in the

complex plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the -axis, called the real axis, is formed by the real numbers, and the -axis, called the imaginary axis, is formed by the ...

. He has also contributed improved bounds for the

Erdős–Szemerédi theorem In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set A of integers, at least one of A+A, the set of pairwise sums or A\cdot A, the set of pairwise products form a significantly larger set. More precisely, t ...

, showing that every set of real numbers has either a large set of pairwise sums or a large set of pairwise products, and for the

Erdős distinct distances problem In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015. ...

, showing that every set of points in the plane has many different pairwise distances.

Recognition

In 2006, Solymosi received a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

and in 2008 he was awarded the André Aisenstadt Mathematics Prize. In 2012 he was named a doctor of the

Hungarian Academy of Science The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its ma ...

Selected publications

References

External links

Home page
* {{DEFAULTSORT:Solymosi, Jozsef Year of birth missing (living people) Living people Canadian mathematicians 20th-century Hungarian mathematicians 21st-century Hungarian mathematicians Eötvös Loránd University alumni ETH Zurich alumni University of British Columbia faculty Combinatorialists Graph theorists